ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Pavlov A. N. Wavelet-­analysis and examples of it's applications. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 5, pp. 99-111. DOI: 10.18500/0869-6632-2009-17-5-99-111

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 1591)
Article type: 

Wavelet-­analysis and examples of it's applications

Pavlov Aleksej Nikolaevich, Saratov State University

Theoretical background of the wavelet­analysis and a series of applications of the given method are considered including a study of clustering phenomena for synchronous dynamics in structural units if the kidney, tactile information encoding by neurons of the trigeminal complex and detection of information messages from the chaotic carrying signal.

  1. Grossman A, Morlet J. Decomposition of Hardy functions into square intergable wavelets of constant shape. SIAM J. Math. Anal. 1984;15(4):723–736. DOI: 10.1137/0515056.
  2. Daubechies I. Ten lectures on wavelets. Philadelphia: S.I.A.M.; 1992. 357 p.
  3. Meyer Y. Wavelets: Algorithms and applications. Philadelphia: S.I.A.M.; 1993. 133 p.
  4. Kaiser G. A friendly guide to wavelets. Boston: Birkhauser; 1994. 324 p.
  5. Astafieva NM. Wavelet analysis: basic theory and some applications. Phys. Usp. 1996;39(11):1085–1108. DOI: 10.3367/UFNr.0166.199611a.1145.
  6. Mallat SG. A wavelet tour of signal processing. New York: Academic Press; 1998. 851 p.
  7. Koronovskii AA, Khramov AE. Continuous Wavelet Analysis and Its Applications. Moscow: Fizmatlit; 2003. (in Russian)
  8. Addison PS. The illustrated wavelet transform handbook: applications in science, engineering, medicine and finance. Bristol, Philadelphia: IOP Publishing; 2002. 368 p.
  9. Vetterli M, Kovacevic J. Wavelets and subband coding. New-Jersey: Prentice Hall; 1995. 519 p.
  10. Holstein-Rathlou NH, Leyssac PP. TGF-mediated oscillations in the proximal intratubular pressure: differences between spontaneously hypertensive rats and Wistar-Kyoto rats. Acta Physiol Scand. 1986;126(3):333–339. DOI: 10.1111/j.1748-1716.1986.tb07824.x.
  11. Marsh DJ, Sosnovtseva OV, Pavlov AN, Yip K-P, Holstein-Rathlou N-H. Frequency encoding in renal blood flow regulation. American Journal of Physiology. Regul. Integr. Comp. Physiol. 2005;288(5):1160-1167. DOI: 10.1152/AJPREGU.00540.2004.
  12. Sosnovtseva OV, Pavlov AN, Mosekilde E, Yip K-P, Holstein-Rathlou N-H, Marsh DJ. Synchronization among mechanisms of renal autoregulation is reduced in hypertensive rats. American Journal of Physiology (Renal Physiology). 2007;293(5):1545–1555. DOI: 10.1152/ajprenal.00054.2007
  13. Moreno A, Garsia-Gonzalez V, Sanches-Jimenez A, Panetsos F. Principalis, oralis and interpolaris responses to whisker movements provoked by air jets in rats. NeuroReport. 2005;16(14):1569–1573. DOI: 10.1097/01.wnr.0000180144.99267.73.
  14. Pavlov AN, Makarov VA, Mosekilde E, Sosnovtseva OV. Application of wavelet-based tools to study the dynamics of biological processes. Brief Bioinform. 2006;7(4):375–389. DOI: 10.1093/bib/bbl041.
  15. Carvell GE, Simons DJ. Task- and subject-related differences in sensorimotor behavior during active touch. Somatosens Mot Res. 1995;12(1):1-9. DOI: 10.3109/08990229509063138.
  16. Garabedian CE, Jones SR, Merzenich MM, Dale A, Moore CI. Band-pass response properties of rat SI neurons. J Neurophysiol. 2003;90(3):1379–1391. DOI: 10.1152/jn.01158.2002.
  17. Pavlov AN. Detection of information signals based on reconstruction of dynamical systems and discrete wavelet-transform. Izvestiya VUZ. Applied Nonlinear Dynamics. 2008;16(6):3–17. DOI: 10.18500/0869-6632-2008-16-6-3-17.
  18. Kocarev L, Halle KS, Eckert K, Chua LO, Parlitz U. Experimental demonstration of secure communications via chaotic synchronization. Int. J. Bifurcation and Chaos. 1992;2(3):709–713. DOI: 10.1142/S0218127492000823.
  19. Cuomo KM, Oppenheim AV, Strogatz SH. Synchronization of Lorenz-based chaotic circuits with application to communications. IEEE Trans. Circuits Syst. 1993;40(10):626–633. DOI: 10.1109/82.246163.
  20. Parlitz U, Kocarev L. Multichannel communication using autosynchronization. Int. J. Bifurcation and Chaos. 1996;6(3):581–588. DOI: 10.1142/S0218127496000278.
  21. Dmitriev AS, Panas AI. Dynamic chaos. New media for communication systems. Moscow: Fizmatlit; 2002. 251 p. (In Russian).
  22. Koronovsky AA, Moskalenko OI, Popov PV, Hramov AE. Method for secure data transmission based on generalized synchronization. Bulletin of the Russian Academy of Sciences: Physics. 2008;72(1):131–135. DOI: 10.1007/s11954-008-1030-7.
  23. Anishchenko VS, Pavlov AN. Global reconstruction in application to multichannel communication. Phys. Rev. E. 1998;57(2):2455–2457. DOI: 10.1103/PhysRevE.57.2455.
Short text (in English):
(downloads: 70)